# Shape Representation as the Intersection of n-k Hypersurfaces

1 ROBOTVIS - Computer Vision and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We investigate the feasibility of representing implicitly a k-dimensional manifold embedded in the Euclidean space $\mathbb{R}^n$ as the intersection of n-k transverse hypersurfaces. From the analytical point of view, the embedded manifold is defined as the inverse image of a regular value of a vector function. This approach is a priori appealing since the corresponding function is differentiable at any point of the embedded manifold. We focus on time-dependent manifolds and establish the link between the velocity field of the evolving manifold and a Partial Differential Equation (PDE) satisfied by its describing function.
Keywords :
Type de document :
Rapport
[Research Report] RR-4011, INRIA. 2000, pp.26
Domaine :

https://hal.inria.fr/inria-00072632
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 10:27:05
Dernière modification le : samedi 27 janvier 2018 - 01:31:09
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:16:17

### Identifiants

• HAL Id : inria-00072632, version 1

### Citation

José Gomes, Olivier Faugeras. Shape Representation as the Intersection of n-k Hypersurfaces. [Research Report] RR-4011, INRIA. 2000, pp.26. 〈inria-00072632〉

### Métriques

Consultations de la notice

## 81

Téléchargements de fichiers